- Li Chen
- Louisiana State University
- Date: Oct. 18, Wednesday, 2023
- Time: 11:00am -- 12:00pm
- Host: Erkan Nane
- Room: Parker 326
- Abstract: We will first introduce fractional Gaussian fields and their regularity properties on the Sierpinski gasket. Such fields are defined via distributions of \[X_{\alpha} = (-\Delta)^{-\alpha}W,\] where \(W\) is a Gaussian white noise and \(\Delta\) is the Laplacian operator on the Sierpinski gasket. Then we will discuss the Parabolic Anderson Model: \[\partial_t u=\Delta u+\beta u\dot{W}_{\alpha},\] where the fractional noise is white in time and colored in space with the spatial covariance being the same as \(X_\alpha\). We will study the existence and uniqueness of solutions in the Ito sense and give their moment estimates. The main analytic tools are heat kernel estimates and spectral theory.